We consider the sensor management problem arising in using a multi-mode sensor to track moving and stopped targets. The sensor management problem is to determine what measurements to take in time so as to optimize the utility of the collected data. Finding the best sequence of measurements is a hard combinatorial problem due to many factors, including the large number of possible sensor actions and the complexity of the dynamics. The complexity of the dynamics is due in part to the sensor dwell-time depending on the sensor mode, targets randomly starting and stopping, and the uncertainty in the sensor detection process. For such a sensor management problem, we propose a novel, computationally efficient, farsighted algorithm based on an approximate dynamic programming methodology. The algorithm's complexity is polynomial in the number of targets. We evaluate this algorithm against a myopic algorithm optimizing an information-theoretic scoring criterion. Our simulation results indicate that the farsighted algorithm performs better with respect to the average time the track error is below a specified goal value.